I have owned several 686s (purchased new in the 1980s) and currently own a 4" 586 no dash and a 6" 586-3. I also still have three Pythons, a 2.5" from 1965, a 4" I bought new in the late 1970s and a 6" stainless from 1989 with a factory tune. I shoot all of them a lot. I can't speak to the shootability of the new Pythons, have only handled and dry fired them at my LGS. My L frames are accurate and have decent actions. All of my Pythons exhibit superior accuracy and have excellent actions. I consider both to be fine revolvers, with an edge to the Pythons. I don't have a new 686, but did purchase a new 2.75" 69 (also an L frame) about a year ago. It is cosmetically decent, but the action is not up to the smoothness of any of my older S&We (of which I have many), and I intend to do an action job on it soon. I also bought a 25-15 a short time ago, and have been very disappointed with it in DA, not smooth, heavy and stacks like crazy. Definitely in need of an action job. Based on that, I'm not likely to buy a new 686. I seriously considered a new 4.25" Python, but decided I didn't really need it. However, if Colt starts to make them available with an 8" barrel, I'll be all in. I was impressed with the smoothness of the new Python double action, and it's single action can be much improved with some light stoning to get more in the range of the original Pythons. I am not impressed with the rear sight of the new Python, but I understand Colt is working on a better sight for it, and there are other sights which can be installed. If price is not an overriding concerb, I would go with a new Python over the new 686. However, it is likeky, based on my recent experience with newS&Ws, that you may need to get an action job on one, effectively raising the net price.
BTW, there is a lot of internet talk about Pythons being weak and going out of time at the drop of a hat. I will admit that in 2010, after 45 years of carry and use, with many thousands of full charge 357 magnums run through it, my 2.5" Python started to go a little bit out of time. I sent it back to Colt's Custom shop and, for the grand sum of $85, they went through the gun, got it running like new, and replaced the rather battered front and rear sights with new red ramp front and white outlive rear, as I requested. What an improved sight picture, and it shoots like a dream. Too bad Colt no longer works on the old DA revolvers. That being said, 45 years of heavy service before needing minor maintenance just doesn't seem to me like it's a weak action. The new Pythons have an entirely different action than the original Pythons, anyway, and are probably no more prone to problems than an S&W.
Honestly, although I love my Smiths(of which I have many) and enjoy them all, if push came to shove, the last guns I would ever let go of would be my Pythons.